All the rods have same conductance ' K ' and same area of cross section 'A'. If ends A and C are maintained at temperature 2 T0 and T0 respectively then which of the following is/are correct?

Question

All the rods have same conductance ' K ' and same area of cross section 'A'. If ends A and C are maintained at temperature 2 T0 and T0 respectively then which of the following is/are correct? (A) Rate of heat flow through A B C, A O C and A D C is same (B) Rate of heat flow through B O and O D is not same (C) Total rate of heat flow from A to C is (3 K A T0/2 a) (D) Temperature at junctions B, O and D are same

Tardigrade Admin · Accepted Answer

By symmetry IA B=IB C and IA D=ID C ∴ No current in B O and O D ∴ TB=TO=TD

Q. All the rods have same conductance ' $K$ ' and same area of cross section ' $A$ '. If ends $A$ and $C$ are maintained at temperature $2 T_{0}$ and $T_{0}$ respectively then which of the following is/are correct?

Rate of heat flow through $A BC, A OC$ and $A D C$ is same

Rate of heat flow through $BO$ and $O D$ is not same

Total rate of heat flow from $A$ to $C$ is $\frac{3 K A T _{0}}{2 a}$

Temperature at junctions $B, O$ and $D$ are same

By symmetry
$I_{A B} = I_{BC}$ and $I_{A D} = I_{D C}$
$∴$ No current in $BO$ and $O D$
$∴ T_{B} = T_{O} = T_{D}$

Q. All the rods have same conductance ' K ' and same area of cross section 'A'. If ends A and C are maintained at temperature 2T0​ and T0​ respectively then which of the following is/are correct?

Rate of heat flow through ABC,AOC and ADC is same

Rate of heat flow through BO and OD is not same

Total rate of heat flow from A to C is 2a3KAT0​​

Temperature at junctions B,O and D are same